Problem 3

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Solution

using System.Collections.Generic;

using System;

namespace ProjectEulerCSharp_002

{

    class Program

    {

        static void Main(string[] args)

        {

            List<long> factors = PrimeFactor(600851475143);

           

            // this sorts the numbers in ascending order

            factors.Sort();

            // this reverses the list so the biggest one

            // is on top.

            factors.Reverse();

 

            //show me the money

            System.Console.WriteLine(factors[0]);

        }

   

 

        public static List<long> PrimeFactor(long number)

        {

            //here is our list of prime factors

            List<long> factors = new List<long>();

           

            //assume the number is prime

            //unless we find a factor

            bool isPrime = true;

 

            //here is the upper limit of what we need to test

            long factorCandidate = (long)Math.Sqrt(number);

            while (factorCandidate > 1)

            {

                //is this a factor?

                if (number % factorCandidate == 0)

                {

                    //if so, what are it’s factors?

                    factors.AddRange(

                        PrimeFactor(factorCandidate));

                    //what about the other divisor?

                    factors.AddRange(

                        PrimeFactor(number / factorCandidate));

                    //we know this one isn’t prime

                    isPrime = false;

                }

                //next

                factorCandidate–;

            }

            //we are only adding prime factors

            if (isPrime) { factors.Add(number); }

            //send ’em back

            return factors;

        }

    }

}

 

Discussion

In contrast to my F# solution this didn’t take much longer than 5 minutes to write.  I didn’t spend any time optimizing it because it ran so fast for the problem already.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).